Howard Miller

Do NOT change moodledata. The needs and should be writeable by the web server (user www-data).

DO change public so something that is not writeable by the web server. Your own username, root, or whatever depending where it is.

No, it will not pull your site offline (if you do it right)

I'm going to suggest that spending an hour or two learning how file ownership and permissions work and how to modify them on your system is time VERY well spent. This kind of issue comes up all the time.

What James said. It's a basic security provision to make sure your program code is locked down.

There have been some 'worms' in the past that can infect Moodle files, so it's a real possibility.

Should the search and replace tool fix that? I don't know - I don't use those menus.

Is the $CFG->wwwroot setting correct in your dev site's config.php file?

and/or, see Search_and_replace_tool